Dr Nicolas Boulle | Cambridge Image Analysis

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I am a Research Fellow in Numerical Analysis.

My research interests lie at the intersection between numerical analysis and deep learning. I primarily focus on the mathematical foundations of deep learning to discover mathematical models (partial differential equations) from data, and the development of novel and theoretically justified numerical techniques.

I am a member of the Scientific Artificial Intelligence (SciAI) Center supported by the Office of Naval Research (ONR).

Publications

Optimization of Hopf Bifurcation Points

N Boullé, PE Farrell, ME Rognes

– SIAM Journal on Scientific Computing

(2023)

45,

B390

(doi: 10.1137/22M1474448)

Principled interpolation of Green's functions learned from data

H Praveen, N Boullé, C Earls

– Computer Methods in Applied Mechanics and Engineering

(2023)

409,

115971

(doi: 10.1016/j.cma.2023.115971)

Elliptic PDE learning is provably data-efficient

N Boullé, D Halikias, A Townsend

(2023)

(link to publication)

Two-component three-dimensional atomic Bose-Einstein condensates supporting complex stable patterns

N Boullé, I Newell, PE Farrell, PG Kevrekidis

– Physical Review A

(2023)

107,

012813

(doi: 10.1103/physreva.107.012813)

Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem

F Laakmann, N Boullé

(2022)

(link to publication)

Principled interpolation of Green's functions learned from data

H Praveen, N Boulle, C Earls

(2022)

(link to publication)

Data-driven discovery of Green's functions

N Boullé

(2022)

(link to publication)

Two-Component 3D Atomic Bose-Einstein Condensates Support Complex Stable Patterns

N Boullé, I Newell, PE Farrell, PG Kevrekidis

(2022)

(link to publication)

Learning Green’s functions associated with time-dependent partial differential equations

N Boullé, S Kim, T Shi, A Townsend

– Journal of Machine Learning Research

(2022)

23,

Bifurcation analysis of two-dimensional Rayleigh-Bénard convection using deflation

N Boullé, V Dallas, PE Farrell

– Phys Rev E

(2022)

105,

055106

(doi: 10.1103/PhysRevE.105.055106)